Juan Mata in Denver, where Manchester United played Roma in a pre-season friendly tournament, the Guinness International Champions Cup. Photograph: Isaiah Downing/Action Images

Juan Mata has admitted that Louis van Gaal showed his first flash of anger after the goals Manchester United conceded in Saturday’s win over Roma, though the Spaniard believes the manager’s demand of perfection is precisely what the team needs.

Mata has emerged as Van Gaal’s first choice as the team’s No10 in his favoured 3-5-2 formation, although the playmaker was among those criticised by Van Gaal after the match.

United defeated Roma 3-2 in Denver in their opening group game of the International Champions Cup. Yet after taking a 3-0 lead into half-time, with two goals from Wayne Rooney and one from Mata, United allowed Roma back into the contest. A 70-yard lob from Miralem Pjanic was followed by Francesco Totti’s late penalty and United ended the match hanging on.

And Van Gaal wasted no time in informing his team they cannot afford to be so sloppy in future. “After the game when we had given two goals away he was not very happy, but I think his way is that of a great manager,” Mata said, before emphasising that all of the players respect the Dutchman’s approach.

“He is very honest with the players, he says what he thinks and has a clear way of understanding football. We feel the manager is a great manager who has brought a strong mentality. This club is made for a winning mentality and I think he has it.

“He has had success in different countries. We are happy with him and the way he works. Everything is new but we are adapting well to his style of football. He is right to be demanding. As a player you want a coach like this, always demanding more and to play better and try to win the games earlier or in a different way.”

Against Roma, for whom Ashley Cole played as a second-half replacement, United were sluggish, with Van Gaal later blaming the heat of the 2pm kick-off and the mile-high altitude of the stadium. Mata, who is the club’s record £37m signing after joining in January, said: “The first 15 to 20 minutes we played a bit slow and it was difficult because the pitch was dry. But we tried to perform how the manager wants.

“It is my first pre-season with Manchester United and my first tour with the club and I am trying to get ready for the first game, against Swansea.”

Mata believes fans will see his best play in the forthcoming season. “I will try my best, during the season hopefully we can play good football and I can do assists and score goals because that is what I have to do,” he said. “It was difficult last season, when I arrived it was a difficult time for the club. We had changed managers but didn’t get the results.

“But we are starting a new season with a new manager and we aim to put the club back where it deserves to be and that is fighting at the top. Things are changing and everyone is finding their new role in the team. But if I play behind the two strikers I feel comfortable. I have played on the left or right but my best season was when I played in that position under Rafa Benítez [at Chelsea].”

Mata also praised the arrival of Ander Herrera, who has impressed on the tour so far, from Athletic Bilbao. “He is a very, very good midfielder. He is a good guy, my friend, we have known each other since we were 15,” said Mata. “He is top quality, he can play quick, slow, dictate the rhythm of a game. He can score as well. He is a very complete midfielder and can bring these qualities to the team.”

Meanwhile the Roma coach, Rudi Garcia, has indicated that United will have to stump up at least €100m (£79m) if they want to sign Kevin Strootman. Van Gaal had said on Friday he will monitor the Dutchman’s recovery from cruciate ligament surgery before deciding whether to bid for the Holland and Roma midfielder.

Garcia responded by commenting: “What can I say about the rumours. Maybe after a three-digit offer, then we will sit down and think about it.”

Strootman, who Van Gaal knows from his time as Holland manager, missed Saturday’s game in Denver as he is continuing his recovery from an anterior cruciate ligament injury sustained in March.

The 24-year-old is rehabilitating well, according to his manager. “Kevin is following a normal recovery programme. He is fine. He will start running soon,” Garcia added.